Since the ternary intermetallic compound Co3(Al,W) with the L12 structure was discovered, two-phase Co-base alloys composed of the γ-Co solid-solution phase and the γ'-Co3(Al,W) phase as a strengthening phase have been investigated as promising high-temperature materials. Some Co-base alloys have been reported to exhibit high-temperature strength greater than those of conventional Ni-base superalloys. Although the excellent high-temperature physical properties of the Co-based alloys are considered to result from the phase stability and strength of Co3(Al,W), the pristine physical properties of Co3(Al,W) have not been fully understood, supposedly due to the difficulties in obtaining single-phase Co3(Al,W). In the present study, we examine the effect of heat treatment on the microstructure of alloys with compositions close to single-phase Co3(Al,W) as well as their mechanical properties, e.g. elastic modulus, thermal expansion, etc., in hope of deriving the pristine properties of the Co3(Al,W) phase. A single crystal with the composition of Co-10Al-11W grown by floating-zone melting exhibits a thermal expansion coefficient of 10×10-6 K-1 at room temperature, which is virtually identical to those of the commercial Ni-base superalloys. However, it increases with increasing temperature followed by a discontinuity at around 1000°C, inferring the phase transformation from γ' to γ. The investigated thermal expansion behavior indicates that the lattice mismatch between the γ' and γ phases is reversed from positive at room temperature to negative at high temperatures above around 500°C. The results of elastic property measurement and environmental embrittlement investigation of polycrystalline Co3(Al,W) will also be presented.